India was about as poor as countries like South Korea immediately post world war 2. The most massive difference was their embrace of a Soviet style planned economy, which means that they grew at about 1-2% annually for the next 40 years and South Korea grew at a much, much higher rate. It's not a coincidence that economic liberalization in India in the early 90s (as with china, 15 years earlier) coincided with a boom in growth rate.

I fully agree with your point that India ideally should be many, many countries: democracy suffers greatly when a massive, linguistically, religiously, and culturally diverse subcontinent is forced into a single government. Just look at Europe and their cautious, precarious tiptoeing towards political unity, despite having the relative advantage of being infinitely less diverse, way less religious, and way more developed than the Indian subcontinent.